Welcome to the WSU Vancouver Seminar in Mathematics
and Statistics! The Seminar meets on Wednesdays at
1:10-2 PM in VLIB 240. This is the building marked
"H" in the campus
map, and is near the Undergraduate building
(marked "N") where all Math/Stat faculty have
offices. The seminar is open to the public, and here
is some information
for visitors.

Students could sign up for Math 592 (titled
Seminar in Analysis) for 1 credit. Talks will be given
by external speakers, as well as by WSUV faculty and
students. Contact the organizer Bala Krishnamoorthy if you
want to invite a speaker, or to give a talk.

Abstract (click to read)

One of the first mathematical concepts we learn as
children is counting, and when we do so, we think
of counting the number of elements in a specific
set. Soon after, we forget about sets and we just
consider the abstract numbers themselves. This
abstraction simplifies many things, but it also
makes us forget about some structure that we had
when we were thinking about sets. That structure
can be encoded by a category. In this talk we will
describe certain concepts in category theory, and
you will realize that in most of your mathematics
classes you have been working with categories, you
just didn't know about it. There will be plenty of
examples that will show that category theory
provides a unifying language for mathematics, and
that many constructions are more naturally
understood when they are seen through the
categorical lens.

Abstract (click to read)

A problem faced by all perceptual systems is
natural variability in sensory stimuli associated
with the same object. This is a common problem in
sensory perception: Interpreting varied optical
signals as originating from the same object
requires a large degree of tolerance
[1]. Understanding
speech requires identifying phonemes, such as the
consonant /g/, that constitute spoken words. A /g/
is perceived as a /g/, despite tremendous
variability in acoustic structure that depends on
the surrounding vowels and
consonants [2]. A
major goal of an object recognition problem then
is the ability to identify individual objects
while being invariant to changes stemming from
multiple stimulus transformations.

In an ongoing project [3],
we are testing the hypothesis that broad
perceptual invariance is achieved through specific
combinations of what we term locally invariant
elements. The main questions we would like to
address are: 1. What are the characteristics of
locally-invariant units in sensory pathways?
2. How are biological locally-invariant units
combined to achieve broadly invariant percepts?
3. What are the appropriate mathematical
structures with which to address and model these
sensory processes? The mathematical aspects of
the research involve an interesting combination of
probability theory (a must in the study of
biological sensory systems) and group theory,
needed to characterize invariants and symmetries.

The parameterization of PPA formulas Using a SORTIE-ND
model for Harvard forest

Abstract (click to read)

Spatially-implicit forest growth models, such as
the perfect plasticity approximation (PPA), allow
for the computationally efficient scaling of
forest dynamics to the landscape scale, by using
simplified mechanisms of individual tree
competition. The parameterization and calibration
of PPA using empirical data is challenging,
limiting its applications in biogeochemistry and
forest modeling. In contrast, the statistical
methodology for parameterization of spatially
explicit individual-based forest models, such as
SORTIE, is well developed. In this work we
parameterize the spatially-implicit PPA model by
calibrating the spatially-explicit SORTIE-ND model
using Harvard forest as a test site. Despite the
two models using different tree competition
mechanisms, both predicted similar biomass
dynamics. Community composition diverged in the
two models: between an Eastern hemlock dominated
system in SORTIE-ND and a red maple dominated in
PPA. This illustrates that the different
competition mechanisms employed in
spatially-explicit and -implicit models can lead
to different predictions of forest successions,
and provides a method for an initial
parametrization of PPA using SORTIE-ND which is
sufficient for scaling of biomass dynamics, but
requires further calibration for species dynamics.

Abstract (click to read)

The classical paradigm for null hypothesis
significance testing has suffered from
misapplication and misinterpretation for many
years but it reached a fevered pitch when the
American Statistical Association issued a
statement on p-values in 2014. In this talk we
will consider an approach to formulating classical
inference that is expressive of the underlying
concepts. This approach is implemented
in infer,
a new package for the R statistical language.